论文标题
许多边缘和最大程度有限的集团
Many cliques with few edges and bounded maximum degree
论文作者
论文摘要
在过去的几十年中，普遍的Turán问题一直是极端组合学研究的中心主题。一个问题是，最近通过Chase完全解决了具有固定数量的顶点和有界最大程度的图表中固定顺序数量的数量。 Kirsch和Radcliffe提出了此问题的自然变体，其中边缘数是固定的而不是顶点的数量。在本文中，我们确定了固定顺序的最大数量，该固定顺序具有固定数量的边缘数量和有限的最大程度，从而解决了Kirsch和Radcliffe的猜想。我们还给出了极端图的完整表征。
Generalized Turán problems have been a central topic of study in extremal combinatorics throughout the last few decades. One such problem, maximizing the number of cliques of a fixed order in a graph with fixed number of vertices and bounded maximum degree, was recently completely resolved by Chase. Kirsch and Radcliffe raised a natural variant of this problem where the number of edges is fixed instead of the number of vertices. In this paper, we determine the maximum number of cliques of a fixed order in a graph with fixed number of edges and bounded maximum degree, resolving a conjecture by Kirsch and Radcliffe. We also give a complete characterization of the extremal graphs.
